Crystal formation modeling

A dense-bed center-fed column (Fig. 22-li) having provision for internal crystal formation and variable reflux was tested by Moyers et al. (op. cit.). In the theoretical development (ibid.) a nonadiabatic, plug-flow axial-dispersion model was employed to describe the performance of the entire column. Terms describing interphase transport of impurity between adhering and free liquid are not considered. 

Figure 5.6. Cell types that may be used in modeling crystal formation...

CA in which many filled cells execute a random walk but never interact with one another, cannot give rise to stable pattern formation since the cells will move at random forever. However, if cells can interact when they meet, so that one diffusing cell is allowed to stick to another, stable structures can be created. These structures illustrate the modeling of diffusion-limited aggregation (DLA), which is of interest in studies of crystal formation, precipitation, and the electrochemical formation of solids. 

Fig. 31 Structural formation model for the initial stage of polymer crystallization [19], N G nucleation and growth of oriented domains, SD spinodal decomposition into oriented and unoriented domains, Tb, Ts, and Tx bimodal, spinodal, and crystallization temperatures, respectively I isotropic, N smectic, and C crystalline...

Vanadium(n) Complexes.—Dehydration of VSO. THjO has been shown to proceed via the formation of VS04,mH20 (where n = 6, 4, or 1) and V(OH)-(SO4), which were characterized by X-ray studies. The polarographic behaviour and the oxidation potential of the V -l,2-cyclohexanediamine-tetra-acetic acid complex, at pH 6—12, have been determined.Formation constants and electronic spectra have been reported for the [Vlphen),] " and [V20(phen)] complexes. The absorption spectrum of V ions doped in cadmium telluride has been presented and interpreted on a crystal-field model. The unpaired spin density in fluorine 2pit-orbitals of [VF ] , arising from covalent transfer and overlap with vanadium orbitals, has been determined by ENDOR spectroscopy and interpreted using a covalent model. " ... 

In the formation model of the above hydrate concentrations, Torres et al. (2004) indicate that the pressure of hydrate crystallization can exceed the overburden pressure. This can occur at shallow subseafloor depth, to cause massive hydrate deposits such as those shown in Figure 7.28, if hydrates do not promptly cement the grains. This finding is similar to that observed by Sassen and coworkers in the Gulf of Mexico (Personal Communication, November 10, 2005). Torres and coworkers also suggest that methane dissolved in water alone is insufficient to cause the noted hydrate concentrations—there must be additional free gas present. 

In this paper, we make use of molecular modelling techniques, particularly the AMI semiempirical molecular orbital method, to study the intermolecular interactions that are important for determining the manner in which crystal formation takes place. We are particularly inter ested in compounds that can potentially exhibit nonlinear optical properties. The calculational techniques are directed towards providing insight into the manner in which the desired nonlinear optical properties can be op timized in the macromolecular crystal state.(1)... 

---